### Abstract

We consider the problem of constructing Wannier functions for Z_{2} topological insulators in two dimensions. It is well known that there is a topological obstruction to the construction of Wannier functions for Chern insulators, but it has been unclear whether this is also true for the Z _{2}case. We consider the Kane-Mele tight-binding model, which exhibits both normal (Z_{2}-even) and topological (Z_{2}-odd) phases as a function of the model parameters. In the Z_{2}-even phase, the usual projection-based scheme can be used to build the Wannier representation. In the Z_{2}-odd phase, we do find a topological obstruction, but only if one insists on choosing a gauge that respects the time-reversal symmetry, corresponding to Wannier functions that come in time-reversal pairs. If, instead, we are willing to violate this gauge condition, a Wannier representation becomes possible. We present an explicit construction of Wannier functions for the Z_{2}-odd phase of the Kane-Mele model via a modified projection scheme, followed by maximal localization, and confirm that these Wannier functions correctly represent the electric polarization and other electronic properties of the insulator.

Original language | English (US) |
---|---|

Article number | 035108 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 83 |

Issue number | 3 |

DOIs | |

State | Published - Jan 13 2011 |

### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics

## Fingerprint Dive into the research topics of 'Wannier representation of Z<sub>2</sub> topological insulators'. Together they form a unique fingerprint.

## Cite this

_{2}topological insulators.

*Physical Review B - Condensed Matter and Materials Physics*,

*83*(3), [035108]. https://doi.org/10.1103/PhysRevB.83.035108